For a while I did this to get rid of the notifications: I changed my google password on the computer. Voila. No new mail on the phone. ha ha
If you keep it unsynced, and keep notifications off, changing the password won't be necessary.
However, today I updated the password (to send some pics from the phone to myself, as I don't know how else to do it),
The best way is some sort of cloud storage app. There's Google Drive, but if you want to get away from Google services, Dropbox is a great option. You install it on your computer and your phone, and all you have to do is place whatever in your Dropbox (from either your computer or your phone) and it's accessible from anywhere.
and noticed that the battery seems to discharge a lot quicker.
Having Gmail, or any such app synced shouldn't put much of a drain on the battery at all. The 2 main battery drainers are using 3G/4G or wifi data and the screen. Simply having the screen on takes 60-90% of your battery, depending on what else you're doing. And then if you're using data - like web browsing, poking around eBay or Amazon, or uploading/downloading, that's a big battery drainer (although the screen is the primary battery killer). Simply having wi-fi on drains minimal battery - it only drains significantly when actually being used to transmit data.
Then, I got thinking about data mining and all those privacy issues, and I wondered if I really need that gmail crap on my phone to begin with. Then, the phone tells me that the only way to delete gmail is to go back to the factory settings.
The other stuff ("rooting" for example) is way over my head..
Just unsync Gmail. You don't need to unsync anything else you might have, such as a weather app, or Facebook, Words With Friends. Data mining is mostly harmless, even for the most paranoid, but with Google, some is inevitable. However, most of the time, you can "opt-out" of such things. Obviously, some data mining is used for advertising. Most is merely for apps or websites that you can use to make your life easier, if you use them (like Google Now, or Maps).
If you want to avoid data mining, go into any Google branded app (go to your main Settings, tap Apps or Manage Apps), and reset data on all them. If you use any of those apps, you may get a prompt to allow Google services to collect data, and then you opt-out. Use a different browser than the default or Chrome, or go into the settings of Chrome and opt-out of any data mining. If you're really paranoid, you can turn off the Locator Services (GPS), since this allows Google to know where you are, but IMO, that's pointless and counter-productive to owning a smartphone. So Google knows where you are. BFD. If you need to find a place on a map, or wonder how the weather will be in 3 hours, you need GPS services.